Answer:
[tex]y = -\frac{5}{3}x+\frac{2}{3}[/tex]
Step-by-step explanation:
Given
[tex]f(-2) = 4[/tex]
[tex]f(1) = -1[/tex]
Required
The equation of the function
The given parameters means that:
[tex](x_1,y_1) = (-2,4)[/tex]
[tex](x_2,y_2) = (1,-1)[/tex]
Calculate the slope (m)
[tex]m = \frac{y_2 -y_1}{x_2 -x_1}[/tex]
[tex]m = \frac{-1-4}{1--2}[/tex]
[tex]m = \frac{-5}{3}[/tex]
The equation is then calculated using:
[tex]y = m(x - x_1) + y_1[/tex]
This gives:
[tex]y =\frac{-5}{3}(x--2)+4[/tex]
[tex]y =\frac{-5}{3}(x+2)+4[/tex]
Open bracket
[tex]y = -\frac{5}{3}x-\frac{10}{3}+4[/tex]
Take LCM
[tex]y = -\frac{5}{3}x+\frac{-10+12}{3}[/tex]
[tex]y = -\frac{5}{3}x+\frac{2}{3}[/tex]
Problem 12
Given 12 consecutive integers, in how many ways can three of these integers
be selected to give a sum which divides by 4?
A step by step explanation.
9514 1404 393
Answer:
55
Step-by-step explanation:
Here's one way to count them.
12 consecutive integers will have 3 each of the integers whose value is 0, 1, 2, or 3 mod 4. To make a total that is 0 mod 4, any of these combinations of mod 4 values may be used:
000 -- 1 combination
013 -- 27 combinations, 3 each of mod 0, mod 1, and mod 3
022 -- 9 combinations, 3 of mod 0, and 3 ways to choose 2 of mod 2
112 -- 9 combinations, 3 of mod 2, and 3 ways to choose 2 of mod 1
233 -- 9 combinations, 3 of mod 2, and 3 ways to choose 2 of mod 3
__
Consider the set of 12 consecutive integers 1 .. 12. Then here are the 9 "233" combinations. Mod 2 integers are 2, 6, 10, and mod 3 integers are 3, 7, 11.
(2, 3, 7), (2, 3, 11), (2, 7, 11),
(3, 6, 7), (3, 6, 11), (6, 7, 11),
(3, 7, 10), (3, 10, 11), (7, 10, 11)
The total number of combinations that will be divisible by 4 is ...
1 + 27 + 9 + 9 + 9 = 55 . . . . combinations with a sum divisible by 4
__
Additional comment
The number of ways that 3 can be chosen from 12 is 220, so this is 1/4 of that total. It is perhaps not surprising that the remainders from division by 4 are uniformly distributed among the possibilities.
A computer program to list the 220 subsets and the mod 4 remainders of their totals confirms this is the correct number.
There are [tex]55[/tex] ways of these integers be selected to give a sum.
Given that:
It has consecutive integers .
Now,
Address the formula for [tex]C(n,r)[/tex],
[tex]C(n,r)=\frac{n!}{(n-r)!n!}[/tex]
Here,
[tex]n=12,r=3[/tex]
[tex]C(12,3)=\frac{12!}{(12-3)!3!} \\\\C(12,3)=\frac{12!}{9!3!} \\\\C(12,3)=\frac{12*11*10*9*8*7*6*5*4*3*2*1}{9*8*6*7*5*4*3*2*1*3*2*1} \\\\C(12,3)=\frac{12*11*10}{3*2*1} \\\\C(12,3)=4*5*11\\\\C(12,3)=220[/tex]
The sum [tex]mod 4[/tex] of any given subset increases by [tex]1[/tex] when the set is “slid” to the left.
Every subset gives rise to all four values [tex]mod 4[/tex] by sliding each of four places.
Since, The sum of the integer is divides by [tex]4[/tex].
Thus,
[tex]220\div 4=55[/tex]
Hence, it has [tex]55[/tex] ways .
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In Act I, scene ii, Claudius’s mention of Fortinbras raises the issue of _____. the cause of King Hamlet’s death how Fortinbras is better than Hamlet an external threat to Denmark corruption in Denmark’s government
Answer:
the answer to this is D "an external threat to Denmark"
Step-by-step explanation: just did the assignment :)
Analyze the graph below and complete the instructions as follows.
Answer:
Option A:
x^2 + (y - 2)^2 = 9
Step-by-step explanation:
We know that the equation for a circle centered in the point (a, b) and of radius R is given by:
(x - a)^2 + (y - b)^2 = R^2
So the first thing we need to find is the center of the circle.
We can see that the center is at:
x = 0
y = 2
Then the center is at the point (0, 2)
Now we want our circle to pass through point 2, located at a distance of 2 units from the radius of the first circle.
So the distance between the center and point 2 is 2 units plus the radius of the smaller circle:
And the radius of the smaller circle is one unit.
Then, the radius of a circle centered at (0, 2) that passes through point 2 is:
R = 1 + 2 = 3
Then we have a circle centered at (0, 2) and of radius R = 3
Replacing these in the equation for a circle we get:
(x - 0)^2 + (y - 2)^2 = 3^2
x^2 + (y - 2)^2 = 9
The correct option is A
In a shoe factory, 2.4% shoes made are defective. If the company made 10,000 shoes then the number of defective pieces are
john had a bag of 10 marbles (2 Green, 4 Blue, 1 Yellow, 2 Red) What is the probability that john selects a green marble, replaced it, and then selects a green marble?
Answer:
2/9
Step-by-step explanation:
the question didnt say replaced it with another colour
7 - 9m = 11
explain step by step
Answer:
[tex]m=-\frac{4}{9}[/tex]
Step-by-step explanation:
Given:
[tex]7-9m=11[/tex]
Subtract 7 from both sides
[tex]-9m=4[/tex]
Divide both sides by -9 to get m alone
[tex]m=-\frac{4}{9}[/tex]
Hope this is helpful
Mummy is 32 years older than her daughter, Aliyah. However, she is 8 years younger than daddy. The total age of the three of them is 144. What is daddy's age? 6
Answer:
Father's age = 64 years
Step-by-step explanation:
Given:
Mummy's age = Aliyah's age + 32
Father's age = Mummy's age + 8
Tota age = 144
Find:
Father's age
Computation:
Assume;
Aliyah's age = a
So,
Mummy's age = a + 32
Father's age = a + 32 + 8
Father's age = a + 40
Aliyah's age + Mummy's age + Father's age = Total age
a + a + 32 + a + 40 = 144
3a + 72 = 144
3a = 144 - 72
3a = 72
a = 24
Father's age = a + 40
Father's age = 24 + 40
Father's age = 64 years
Given F ( x ) = -2/3 x - 4 What is the zero of this function?
Answer:
-4
Step-by-step explanation:
f(0)=(-2/3)(0) - 4
= - 4
PLEASE HELP!! graph the circle whose equation is (x-6)^2 + (y+2)^2 =4
Answer:
Y= -x^2+12x-36
Step-by-step explanation:
if a + b + c = 1, ab + bc + ca = -1 and abc = -1. find the value of a³+b³+c³
Answer:
1
Step-by-step explanation:
→ If we know that 3 numbers need to multiply to make -1, it must be
1, 1 and -1
→ Then we just substitute this into a³ + b³ + c³
1³ + 1³ + (-1)³ = 2 - 1 = 1
Question:
The researcher wants to calculate the bacterial count in the dish after x hours of growth.
Fill in the values of A and b to write an exponential expression to model the number of bacteria in a colony that begins
with a single cell and doubles in size every hour
A(b)^x
Answer:
1(2)^x
Step-by-step explanation:
(^x means x is an exponent.)
Since the experiment begins with a single cell, the initial value, A, is 1. The population increases by a factor of 2 every hour, so the growth factor, b, is 2. Substitute the values of A and b in the general form of an exponential expression to create the expression modeling the number of bacteria in the colony after x hours.
A(b)^x=1(2)^x
=2^x
The exponential expression to model the number of bacteria in a colony that begins with a single cell and doubles in size every hour is [tex]1 * 2^{x}[/tex].
What is exponential expression?Exponential expressions are just a way to write powers in short form. The exponent indicates the number of times the base is used as a factor.
Let number of hours be x hours.
The bacterial count in the dish after x hours of growth is [tex]1 * 2^{x}[/tex].
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Help me calculate Lim for this lesson
Answer:
I'm acutally not too sure on this but give me a moment to solve this
Step-by-step explanation:
Which function is a translation of the parent absolute value function?
f(x) = 2x1
f(x) = |x+6| f(x)=|x| f(x)=-4|x|
15 + 36 not-equals 41, so those lengths will not form a triangle.
15 squared + 36 squared = 1,521
41 squared = 1,681
Since a squared + b squared not-equals c squared, it will not be a right triangle.
15 squared + 36 squared = 297
41 squared = 82
Step-by-step explanation; did it on the website euphoria
The translation of the parent function is f ( x ) = | x + 6 | which is shifted 6 units to the left
How does the transformation of a function happen?The transformation of a function may involve any change.
Usually, these can be shifted horizontally (by transforming inputs) or vertically (by transforming output), stretched (multiplying outputs or inputs), etc.
If the original function is y = f(x), assuming the horizontal axis is the input axis and the vertical is for outputs, then:
Horizontal shift (also called phase shift):
Left shift by c units: y=f(x+c) (same output, but c units earlier)
Right shift by c units: y=f(x-c)(same output, but c units late)
Vertical shift:
Up by d units: y = f(x) + d
Down by d units: y = f(x) - d
Stretching:
Vertical stretch by a factor k: y = k × f(x)
Horizontal stretch by a factor k: y = f(x/k)
Given data ,
Let the transformation of the function be a translation , where
The parent function is f ( x ) = | x |
And , the translated function is f ( x ) = | x + 6 |
So , original function is y = f(x), assuming the horizontal axis is the input axis and the vertical is for outputs, then:
Horizontal shift (also called phase shift):
Left shift by c units: y=f(x+c) (same output, but c units earlier)
And , the function is translated 6 units to the left
Hence , the translated function is f ( x ) = | x + 6 |
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The figure below is made of 2 rectangular prisms.
What is the volume of this figure?
Answer:
6536 cubic in
Step-by-step explanation:
1. Split both the prisms apart- In doing so, you can simplify the problem.
2. Put in the #'s for the formula which in this case is V=L*W*H, we will start with the formula for the front one, V=7*8*1 or V=7*8
3. answer for the front is 56 cubic in, now we solve for the other half.
4. V=9*1*90 or V=9*90 which is 6480 cubic in.
5. add 6480 and 56 and your answer is 6536 cubic in as your answer.
Hope this helped ;D
2 Nik owns a stationery shop.
She bought 72 pencils for a total cost of £4.68
Nik sells all 72 pencils for 15p each.
Work out Nik's percentage profit.
Give your answer correct to 1 decimal place.
Answer:
Nik's percentage profit was of 130.8%.
Step-by-step explanation:
Percentage profit:
Profit multiplied by 100% and divided by the price she bought.
Bought:
72 pencils for a total cost of £4.68
Sold:
72 pencils for £0.15 each, so:
72*0.15 = 10.8.
Profit of:
10.8 - 4.68 = 6.12
Percentage profit:
6.12*100%/4.68 = 130.8
Nik's percentage profit was of 130.8%.
Joseph borrows $10000 from his sister Katie at an annual interest rate of 10%. If the
interest is compounded twice a year, how much does he owe after 12 months? Give your answer in dollars.
Answer:
A = P ( 1 + r / n) ^( t * n)
where
A = the amt owed
P = amt borrowed
r = the interest rate as a decimal
n = the number of compoundings per year
t = the number of years
A = 10000 ( 1 + .10 / 2)^(2 *1) = 10000 ( 1.05)^2 = $11025
Step-by-step explanation:
A 15-day supply of vitamins costs $1.74, what is the price in cents per day?
Answer:
it costs 12 cents per day.
Step-by-step explanation:
15 days cost $1.74
1 day then costs 1.74/15 = $0.116 ≈ $0.12
Does this graph show a function? Explain how you know.
PLZ HELP ASAPPP
Answer:
the correct answer is b
Step-by-step explanation:
a function can not have 2 of the same x values for a line on a graph as shown in the picture drawn that i have attached if you need a further explanation let me know
Helppppp pleaseeee
Fill in the blank by entering just a number for your answer.
Check the picture below.
Which best explains whether a triangle with side lengths 2 in., 5 in., and 4 in. is an acute triangle?
The triangle is acute because 22 + 52 > 42.
The triangle is acute because 2 + 4 > 5.
The triangle is not acute because 22 + 42 < 52.
The triangle is not acute because 22 < 42 + 52.
9514 1404 393
Answer:
The triangle is not acute because 2² + 4² < 5²
Step-by-step explanation:
The square of the hypotenuse of a right triangle with the given short sides would be 2² +4² = 20. So, that hypotenuse would be √20, about 4.47. The long side of this triangle is longer than that, so the angle opposite is larger than 90°. The triangle with sides 2, 4, 5 is an obtuse triangle.
The triangle is not acute because 2² + 4² < 5²
The triangle is not acute because 22 + 42 < 52.
Option C is the correct answer.
What is a triangle?A triangle is a 2-D figure with three sides and three angles.
The sum of the angles is 180 degrees.
We can have an obtuse triangle, an acute triangle, or a right triangle.
We have,
To determine if a triangle is acute, we need to check whether all three angles of the triangle are acute angles (less than 90 degrees).
Pythagorean theorem,
- If the square of the length of the hypotenuse is greater than the sum of the squares of the other two sides, then the triangle is acute.
- If the square of the length of the hypotenuse is less than the sum of the squares of the other two sides, then the triangle is obtuse.
Now,
The triangle with side lengths 2 in., 5 in., and 4 in. is not a right triangle.
So we can't use the Pythagorean theorem directly.
Now,
We can check if the sum of the squares of the two shorter sides is greater than the square of the longest side.
2² + 4² = 4 + 16 = 20
5² = 25
Since 20 < 25, we know that the triangle is not acute.
Therefore,
The triangle is not acute because 22 + 42 < 52.
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Suppose that next year the U.S. will be in one of the following economic conditions: Boom, Moderate Growth, Recession, or Depression. The probability that each economic condition will occur, and that a jewelry store will earn profits within that broader economic condition are listed below:
Economic Condition Probability. Jewelry Store Profits
Boom 0.40 $400,000
Moderate Growth 0.30 $300,000
Recession 0.20 $100,000
Depression 0.10 -$500,000
The standard deviation of the jewelry store's profits next year is
A brick staircase has a total of 17 steps The bottom step requires 131 bricks. Each successive step requires 5 less bricks than the prior one. How many bricks are required to build the staircase?
Answer: 1547 bricks are required to build the staircase.
Step-by-step explanation:
We are given:
Number of bricks in the first step, [tex]a_1[/tex] = 131
Number of bricks in the second step, [tex]a_2[/tex] = 131 - 5 = 126
Number of bricks in the third step, [tex]a_3[/tex] = 126 - 5 = 121
Sequence become:
131, 126, 121, .....
These are in arithmetic progression where a = 131 and d (common difference) = -5
To calculate the sum of an AP, we use the formula:
[tex]S_n=\frac{n}{2}[2a+(n-1)d][/tex]
where,
n = number of terms = 17
Putting values in above equation, we get:
[tex]S_n=\frac{17}{2}[2(131)+(17-1)(-5)]\\\\S_n=\frac{17\times 182}{2}=1547[/tex]
Hence, 1547 bricks are required to build the staircase.
in a club there are seven women and five men. A committee of 3 women and 2 men as to be chosen. how many different possibilities are there?
Answer:
Step-by-step explanation:
Find the equation of the straight line that passes through the points (1, 10) and (3, 2)
ANSWER ASAP
Answer:
y = -4x + 14
Step-by-step explanation:
using the slope intercept form of a line
y = mx + c
Given points
1, 10 3, 2slope (m) =
[tex] = \frac{y2 - y1}{x2 - x1} \\ = \frac{2 - 10}{3 - 1} \\ = \frac{ - 8}{2} \\ = - 4[/tex]
taking one point as for filling x and y and finding the y intercept (c)
y =mx + c
10 = (-4) × 1 + c
10 + 4 = c
14 = c
therefore the equation is
y = -4x + 14
Answer:
2y + 8x = 28
Step-by-step explanation:
Hi there
So we are going to solve this together
m = y - y1/y2- y1 =x - x1/x2 - x1
y - 10/ 2- 10 =x - 1/ 3 -1
y -10/-8 =x - 1/2
cross multiply
2(y - 10) =-8(x -1)
2y - 20= -8x + 8
Collect terms
2y +8x = 8 +20
ANSWER = 2y + 8x = 28
Hope this helps you!
Bye , have a nice day :-)
The perimeter of a rectangle is 58 inches and the area is 180 square inches. Find the dimensions of the rectangle.
Answer:
width = 9 inches
length= 20 inches
perimeter of the rectangle=2(9+20)
2w +2L= 2×29
=58 inches
area of the rectangle=w×L
=9×20=180 inch²
A meteorologist records the number of clear days in a given year in each of 21 different U.S. cities. The results are shown below. Find the midrange. 72 143 52 84 100 98 101 120 99 121 86 60 59 71 125 130 104 74 83 55 169
Answer:
Midrange = 85 (Approx.)
Step-by-step explanation:
Given:
72 143 52 84 100 98 101 120 99 121 86 60 59 71 125 130 104 74 83 55 169
Find:
Midrange
Computation:
Number of data = 21
Midrange = [72 + 143 + 52 + 84 + 100 + 98 + 101 + 120 + 99 + 121 + 86 + 60 + 59 + 71 + 125 + 130 + 104 + 74 + 83 + 55 + 169] / 21
Midrange = 1,786/21
Midrange = 85 (Approx.)
Solve for x. 8x = 35
Answer:
[tex]x = \frac{35}{8} [/tex]
Step-by-step explanation:
Divide both sides by 8:
[tex] \frac{8x}{8} = \frac{35}{8} \\x= \frac{35}{8} [/tex]
HCF of the numbers divisible be
3 between 21 and 30 is ___
Answer:
3
Step-by-step explanation:
Numbers between 21 and 30 divisible by 3 are 24 and 27. so you get the HCF of the two.
[tex]\int _{2.2}^{+\infty \:}\frac{10.648}{x^2}[/tex]
Step-by-step explanation:
[tex]\int _{2.2}^{+\infty \:}\frac{10.648}{x^2}dx = 10.648 \int _{2.2}^{\infty \:}\frac{dx}{x^2}[/tex]
[tex] = - \frac{10.648}{x} | _{2.2}^{ \infty} = 4.84[/tex]
the angle between two radii of a circle is 130°. then the angle between the tangents at the end points of radius at their point of intersection is
Answer:
the answer is =180° - 130° = 50°.
Step-by-step explanation:
Hope it helps
Answer:
50 degrees
Step-by-step explanation:
the sum of all angles in a four-sided shape is 360 degrees.
our four points here are :
the center of the circle
the 2 points on the circle, where the 2 tangents touch the circle
the intersection point of the tangents (where they cross each other).
at the 2 points, where radius meets tangent, we have a right angle or 90 degrees. so, they together take already 180 degrees.
the angle at the center of the circle is 130 degrees.
so, all that is left for the angle at the tangent intersection point is
360 - 180 - 130 = 50 degrees